In the Two-Headed Giant format, you still only have to pay once per creature.

Unless some effect explicitly says otherwise, a creature that can't attack you can still attack a planeswalker you control.

The basic land types are Plains, Island, Swamp, Mountain, and Forest. Land types other than basic land types (such as Desert) don't contribute to domain abilities.

Domain abilities count the number of basic land types among lands you control, not how many lands you control or how many of any type.